Characterization of a hyperperfect group

Authors

  • Saugata Purkayastha Gauhati University, Assam, India
  • Dr. Jituparna Goswami Gauhati University, Assam, India
  • Bhargab Debnath Gauhati University, Assam, India

DOI:

https://doi.org/10.11113/matematika.v33.n1.861

Abstract

In this work, we have introduced the notion of hyperperfect group. A group of order n is said to be hyperperfect if there exists a natural number k such that n-1 = k[σ(n)-n-1] where σ(n) denotes the sum of positive divisors of n. We have also established a condition under which a cyclic group is hyperperfect. We have established that no group of prime order is hyperperfect and investigated the same for groups of various non-prime order. We have also determined an upper bound of the order of a hyperperfect group.

Author Biography

Dr. Jituparna Goswami, Gauhati University, Assam, India

Assistant Professor, Dept. of Applied Sciences, Gauhati University Institute of Science and Technology, Guwahati, Assam, India.  Pin-781014

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Published

2017-09-20

How to Cite

Purkayastha, S., Goswami, D. J., & Debnath, B. (2017). Characterization of a hyperperfect group. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 33(1), 97–103. https://doi.org/10.11113/matematika.v33.n1.861

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Articles